Chi-Square Testing 10/23/2012

Readings Chapter 7 Tests of Significance and Measures of Association (Pollock) (pp ) Chapter 5 Making Controlled Comparisons (Pollock Workbook) Chapter 7 Chi-Square and Measures of Association (Pollock Workbook)

OPPORTUNITIES TO DISCUSS COURSE CONTENT

Office Hours For the Week When – Thursday 8-12 – Wednesday 11-1 – And appointment The endorsementendorsement

Course Learning Objectives Students will learn the research methods commonly used in behavioral sciences and will be able to interpret and explain empirical data. Students will learn the basics of research design and be able to critically analyze the advantages and disadvantages of different types of design. As this course fulfills the Computational Skills portion of the University degree plan, students will achieve competency in conducting statistical data analysis using the SPSS software program.

CHI-SQUARE A test of statistical significance

Why Hypothesis Testing To determine whether a relationship exists between two variables and did not arise by chance. (Statistical Significance) To measure the strength of the relationship between an independent and a dependent variable? (association)

Things about Chi-Square It is not a test of strength, just significance Chi-square is inflated by large samples It is a test that tries to disprove the null hypothesis. An insignificant chi-square means that no relationship exists.

Chi-Square is an up or down measure If our significance value is less than or equal to.05 table, we reject the null hypothesis- we have a relationship if our Chi-Square value from our test is greater than.05 we accept the null hypothesis and we have no relationship

HOW TO DO IT IN SPSS

An Easy One Dataset- NES 2008 DV= Who08 IV= Race Null- There is no relationship between Race and Vote in 2008 Alternate- African Americans are More likely to Vote for Obama

First Run A Cross Tab Click on Statistics Click on Chi- Square

The Results What does the Chi-Square Tell us? What is the Asymp. Sig here? What do We Do with the null hypothesis? What is the Practical Significance here?

Hard-Line Immigration Policy D.V. Immigration Policy I.V. Hispanic (dichotomous)

The Results What does the Chi-Square Tell us? What is the Asymp. Sig here? What do We Do with the null hypothesis? What is the Practical Significance here?

What do we have Here?

MEASURES OF ASSOCIATION Nominal Variables

Why Measures of Association Chi-Square only tests for significance It does not say how strongly the variables are related We Use a Measure of Association to Do this

A measure of association is a single number that reflects the strength of the relationship

Measures of association for Nominal Variables tell us: Strength of the Relationship The statistical significance of the relationship These go hand in hand

Measures of Association for Nominal Variables Measure of AssociationRangeCharacteristics Lambda may underestimate, but a PRE measure Phi Use for a 2x2 table only and is Chi-square based Cramer's V Chi-square based and the compliment to PHI.

A value of 1.00 means a perfect relationship, a value of.000 means no relationship

Lambda What kinds of variables are needed for Lambda? Lambda ranges from 0 (no relation) to 1 (a perfect relationship) It measures how much better one can predict the value of each case on the DV if one knows the value of the IV

Interpreting Lambda.000 to.10 none weak moderate strong.40 and above- there is a very strong relationship

Reading Lambda in SPSS IN SPSS, LAMBDA GIVES YOU 3 DIFFERENT VALUES Symmetric- always ignore Two measures of your dependent variable – always use the lambda associated with your dependent variable. – If you place the dependent variable as the ROW VARIABLE, this will be the middle value. Help from Rocky IV. And the videoRocky IVvideo

The one in the middle The significance of the Lambda

Lambda as a PRE Measure Proportional Reduction in Error (PRE) this is defined as the improvement, expressed as a Percentage, in predicting a dependent variable due to knowledge of the independent variable. How well we can predict the dependent variable by knowing the independent variable?

Converting a Lambda to a Percent We take the value of our association measure Multiply by 100% this is our PRE value.

SOME LAMBDA PRACTICE EXAMPLES

Problems with Lambda It fears a TYPE I error so it is very conservative Lambda can Underestimate relationships, even when there are significant chi-square values. If the modal category is even, Lambda is pretty useless.

ALTERNATIVES TO LAMBDA Phi and Cramer’s V

Cramer’s V An alternative to Lambda Ranges from Not a Pre Measure

Phi Measured similarly to Lambda You will use this with 2x2 tables only

An Example Here we can say with a.369 Cramer's V, that we have a very strong relationship between our independent and dependent variables.

Phi And Cramer’s V Interpreting them.000 to.10 none weak moderate strong.40 and above- there is a very strong relationship Limitations Neither are PRE Measures They are both Chi-square based so large samples inflate it

Lambda Underestimating

What the Cramer’s V Tells Us If the Modal category is hard to predict, Lambda falls flat What we see is a weak- to-moderate relationship here. Independents and Democrats are different

Lambda Underestimating Part II D.V.- obama_win08 IV- Region

Lambda shows Nothing We have a moderate relationship, but it is not significant (small sample)

RUNNING LAMBDA, PHI AND CRAMER’S V

Easy to Do How to do it in SPSS Analyze – Descriptive Cross-Tabs – Click on the Statistics Tab Highlight your nominal variable statistics – Choose continue

Two Examples Region and Cig Taxes Region and Public Support for Gay Rights